Highest Common Factor of 698, 964 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 698, 964 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 698, 964 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 698, 964 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 698, 964 is 2.
HCF(698, 964) = 2
HCF of 698, 964 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 698, 964 is 2.
Highest Common Factor of 698,964 is 2
Step 1: Since 964 > 698, we apply the division lemma to 964 and 698, to get
964 = 698 x 1 + 266
Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 266 and 698, to get
698 = 266 x 2 + 166
Step 3: We consider the new divisor 266 and the new remainder 166, and apply the division lemma to get
266 = 166 x 1 + 100
We consider the new divisor 166 and the new remainder 100,and apply the division lemma to get
166 = 100 x 1 + 66
We consider the new divisor 100 and the new remainder 66,and apply the division lemma to get
100 = 66 x 1 + 34
We consider the new divisor 66 and the new remainder 34,and apply the division lemma to get
66 = 34 x 1 + 32
We consider the new divisor 34 and the new remainder 32,and apply the division lemma to get
34 = 32 x 1 + 2
We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 698 and 964 is 2
Notice that 2 = HCF(32,2) = HCF(34,32) = HCF(66,34) = HCF(100,66) = HCF(166,100) = HCF(266,166) = HCF(698,266) = HCF(964,698) .
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Frequently Asked Questions on HCF of 698, 964 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 698, 964?
Answer: HCF of 698, 964 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 698, 964 using Euclid's Algorithm?
Answer: For arbitrary numbers 698, 964 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.